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Mathematics

In the given diagram, RT is a tangent touching the circle at S. If ∠PST = 30° and ∠SPQ = 60° then ∠PSQ is equal to :

  1. 40°

  2. 30°

  3. 60°

  4. 90°

In the given diagram, RT is a tangent touching the circle at S. If ∠PST = 30° and ∠SPQ = 60° then ∠PSQ is equal to : ICSE 2023 Maths Solved Question Paper.

Circles

ICSE 2023

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Answer

We know that,

Angle between tangent and the chord at the point of contact is equal to angle of the alternate segment.

∴ ∠PQS = ∠PST = 30°

In the given diagram, RT is a tangent touching the circle at S. If ∠PST = 30° and ∠SPQ = 60° then ∠PSQ is equal to : ICSE 2023 Maths Solved Question Paper.

In △ PQS,

By angle sum property of triangle,

⇒ ∠PQS + ∠QPS + ∠PSQ = 180°

⇒ 30° + 60° + ∠PSQ = 180°

⇒ ∠PSQ + 90° = 180°

⇒ ∠PSQ = 180° - 90° = 90°.

Hence, Option 4 is the correct option.

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